Szuper began playing hockey in Hungary at an early age, but also showed a flair for the arts. He became an accomplished actor and pianist, but it was between the pipes that he began to achieve prominence. He starred with Ferencvárosi TC as a 16-year-old and led the team to its last domestic title so far. He moved on to the junior team of the Krefeld Pinguine for the 1997–98 season, and had a stellar performance in the 1998 Pool C World Championships.
Moving to North America
Despite his success in Europe, Szuper was pretty unknown when he broke into the Ontario Hockey League in 1998 with the Ottawa 67s. But over the course of the 1998–99 season, Szuper excelled in the net, although he split his time there with Seamus Kotyk. The 67s advanced to the 1999 Memorial Cup as the host team, then defeated the Belleville Bulls in the semifinals to advance to the Memorial Cup championship against the Calgary Hitmen. Ottawa prevailed 7–6 in overtime, and Szuper won the F. W. "Dinty" Moore Trophy as the best rookie goalie of the year. Szuper wasn't picked in the 1999 NHL Entry Draft, so he returned to Ottawa and continued to star. He was then drafted by the Calgary Flames in the 2000 NHL Entry Draft in the 4th round. Szuper would play the next three seasons with the Saint John Flames of the American Hockey League, earning a Calder Cup championship for the 2000–01 season. During the 2002–03 season, Szuper was called up to the NHL with Calgary due to an injury of starting netminder Roman Turek. Szuper dressed for 9 games as the backup for Jamie McLennan, but never played. He is the first Hungarian native to appear on an active NHL roster for a game, but does not appear in the NHL register since he wasn't given any icetime. After failing to stay with Calgary after the 2002–03 season, Szuper was picked by the St. Louis Blues and played in the 2003–04 season in their ECHL affiliate, the Peoria Rivermen.
On January 13, 2012, after playing only one game for the Mavericks, Szuper left the team to sign with the Kazakh team Arystan Temirtau of the Kazakhstan Senior League on January 15, 2012. Szuper was placed on Team Suspension by the Mavericks.
Personal
Szuper lives in his hometown of Budapest. He likes to spend his spare time with his horses on his ranch just outside the city. As a child he was not only an actor, but also a well known dubbing actor and nowadays, after the end of his own season he usually works as a co-commentator during the Stanley Cup playoffs and the World Championships for a Hungarian sports channel. His family name means "super" in Hungarian; due to this his helmets usually include a modified Superman logo with a letter Z.